Let x be the decimal. Multiply by 10, 100 or 1000 so the repeating part lines up, then subtract to remove it. For x = 0.454545…, 100x = 45.4545…, so 99x = 45 and x = 45/99 = 5/11.
If the repeat starts later, as in 0.68181…, use two multiples: 1000x = 681.81… and 10x = 6.81…, so 990x = 675 and x = 675/990 = 15/22. Always simplify the final fraction.
Worked example
Write 0.3̇ (0.333…) as a fraction.
- 10x = 3.333… and x = 0.333…
- 9x = 3, so x = 3/9.
Answer:1/3
Key words
- recurring decimal
- a decimal with a repeating pattern
- exact
- a fraction, not rounded
- dot notation
- dots over the repeating digits
Practise this
New questions every time.
Common Core-referenced: HSN-RN.B.3